Mathematics and Religion: Our Languages of Sign and Symbol.MATHEMATICS AND RELIGION: Our Languages of Sign and Symbol by Javier Leach. West Conshohocken, PA: Templeton Press, 2010. xi + 188 pages, with glossary and index. Paperback; $20.00. ISBN ISBN
International Standard Book Number
ISBN International Standard Book Number
ISBN n abbr (= International Standard Book Number) → ISBN m : 9781599471495.
Conceding that twenty-first century, visually oriented denizens no longer inhabit a literate culture, but seeking to reach out in words to those curious about our human place in the cosmos, the Templeton Science and Religion Series commissions compact scientific/theological explorations of big questions. "Doomed to fail," a skeptic scoffs. "But worth the effort," a sympathetic respondent counters, "if such a text gives, as intended, a good overview of the field for a general audience or rouses the occasional reader to delve more deeply into works on a similar theme."
Connections between mathematics, religion, and metaphysics spark few scholarly fires today. Professional mathematicians never explore such matters as part of their education, and hardly any theologians or philosophers are prepared to follow technical discussions that venture beyond elementary mathematics Elementary mathematics consists of mathematics topics frequently taught at the primary and secondary school levels. The most basic are arithmetic and geometry. The next level is probability and statistics, then algebra, then (usually) trigonometry and pre-calculus. . Nevertheless, a small pocket of readers is interested in all of this on a general level, at least in North America North America, third largest continent (1990 est. pop. 365,000,000), c.9,400,000 sq mi (24,346,000 sq km), the northern of the two continents of the Western Hemisphere. , where the largely evangelical Association of Christians in the Mathematical Sciences continues to flourish.
This book comes out of a very different context and tradition, however. The author is a Jesuit priest who holds an academic position in mathematics and logic at a Spanish university. Trained in mathematics, philosophy, and theology, Javier Leach seems ideally qualified for writing a book on this topic. Drawing upon these disparate backgrounds, he relates religion, science, mathematics, and metaphysics not as antagonists or isolated spheres but as fields sharing common features and interests.
Mathematics and Religion is quite short, shorter even than the bibliographic data above suggests. The body of the text consists of nine brief chapters that run to only 130 pages. The remainder of the book is devoted to a preface (5 pages), ten rather technical appendices (30 pages), a glossary (9 pages), an essay on resources (6 pages), and an index (10 pages). With editorial assistance, the author might have integrated some of his appendices' material into the text (and dropped most of the remainder), but perhaps the publisher judged that enlarging the text proper in this way would reduce sales. Better editing would also have improved the English in a number of places. Readers familiar with idiomatic id·i·o·mat·ic
a. Peculiar to or characteristic of a given language.
b. Characterized by proficient use of idiomatic expressions: a foreigner who speaks idiomatic English. mathematical terminology will find statements such as "m is equal or less than n," [pi] is transcendent," and "odd-grade polynomials with real coefficients have a real number solution" awkwardly phrased or momentarily perplexing per·plex
tr.v. per·plexed, per·plex·ing, per·plex·es
1. To confuse or trouble with uncertainty or doubt. See Synonyms at puzzle.
2. To make confusedly intricate; complicate. .
The first two chapters of the book lay out Leach's overall schematic. Mathematics deals with objects of the mind via logic and formal language. Science deals with objects we perceive with our senses, and it asserts truths about them in representational language, though mathematics and logic are also indispensable. Metaphysics and religion deal with ultimate causes, which mathematics and science are constitutionally unequipped Adj. 1. unequipped - without necessary physical or intellectual equipment; "guerrillas unequipped for a pitched battle"; "unequipped for jobs in a modern technological society" to address. The language of metaphysics and religion employs symbols and terms having personal, communal, and traditional meanings in addition to referring to ultimate realities. Appropriate evidences for the validity of claims in these fields differ, but assertions in each area must strive for consistency; without that, language and thought have no real value.
Chapters three and four give a highly condensed and Eurocentric history of mathematics and logic. Chapter five briefly recounts the rise of modern science, focusing mostly on Galileo, including his conflict with the Roman Catholic church Roman Catholic Church, Christian church headed by the pope, the bishop of Rome (see papacy and Peter, Saint). Its commonest title in official use is Holy Catholic and Apostolic Church. , but giving some attention to Newton and a few later thinkers as well.
With this introductory material out of the way, chapters six and seven focus on the historical and systematic process of formalizing mathematics, and on the rise and contours of mathematical logic. These receive more extended treatment (40 pages), being closest to Leach's area of expertise and relating most directly to the current state of mathematics. Given its broad scope, however, this material contains a number of oversimplifications and omissions. Cantor is portrayed as if he reduced all of mathematics to set theory. Peano is never mentioned for his work on formalization for·mal·ize
tr.v. for·mal·ized, for·mal·iz·ing, for·mal·iz·es
1. To give a definite form or shape to.
a. To make formal.
b. . Brouwer's intuitionism intuitionism
School of mathematical thought introduced by the Dutch mathematician Luitzen Egbertus Jan Brouwer (1881–1966). In contrast with mathematical Platonism, which holds that mathematical concepts exist independent of any human realization of them, intuitionism seems to arise in response to Godel's incompleteness results. Constructive mathematics is claimed to be a subset of classical mathematics. The syntax and semantics of formal logic are presented but with almost no mention of the role deduction systems play in constructing proofs (even though Godel's completeness and incompleteness results touch primarily on deducibility). And so on. These deficiencies may be unavoidable, given the brevity of the text, but such are evidently the consequences of aiming to be so concise while trying to cover such a broad expanse.
Leach ties the fields of mathematics, science, metaphysics, and theology together with the connecting threads of language and logic. As the preface states, "This book is about our languages, ... by which we convey meaning." In all four fields, theories are constructed with language and rely upon logical reasoning. Individually, they share an interest in logical consistency, a concern made prominent by twentieth-century foundations of mathematics. Jointly, they complement each other and offer truths from their own perspectives.
Twentieth-century foundational developments in mathematics (especially incompleteness and undecidability results) also suggest, according to Leach, that mathematics is pluralistic and open-ended. Different perspectives are welcome, as are competing theories. If this is so for our most objective field of thought (and Leach sees this trend in physics as well), we certainly should be open to a variety of complementary perspectives from metaphysics and religion. Room is thus carved out for metaphysics and religion to consider ultimate questions. Mathematics cannot even decide all the important issues in its own field with axiomatic ax·i·o·mat·ic also ax·i·o·mat·i·cal
Of, relating to, or resembling an axiom; self-evident: "It's axiomatic in politics that voters won't throw out a presidential incumbent unless they think his challenger will and foundational methods; it certainly cannot dictate positions outside its purview The part of a statute or a law that delineates its purpose and scope.
Purview refers to the enacting part of a statute. It generally begins with the words be it enacted and continues as far as the repealing clause. .
Complementarity is not due to these areas being totally disjointed. Each field has its own focus, language, and criteria for evidence, but it is a mistake, Leach says, to see them as nonoverlapping. They do not describe different worlds. "Mathematics and science try to answer how things are. Metaphysics and religion try to answer why the world is the way it is" (p. 128). Leach sums up his view of their interrelationships with a model he calls Non-Symmetrical Magisteria: while these fields each have authority in their own domains, they are related through language and logic, albeit in a nonsymmetrical way.
Religious knowledge needs science, while science can do without religion. In effect, this asymmetry is a plus for science by making it autonomous, but it is also a plus for religion by endowing religion with a more comprehensive vision ... [F]aith cannot close its eyes to mathematics and the empirical sciences. I can separate mathematics from theology, but I cannot separate theology from mathematics. Mathematics and the empirical sciences are independent of religious beliefs, but theological reflection cannot do without mathematics and the empirical sciences. (p. 131)
In this way Leach gives a sort of primacy to mathematics and science. In fact, he even says a few pages earlier that "the history of Christianity
Assessing the book's success in relating mathematics and religion depends upon one's own preconceptions of the fields involved and how they are properly linked. The heavy focus on logic and the posited asymmetric relationship between mathematics and religion/philosophy are not universally accepted by historians and philosophers of science and mathematics. Many now conceptualize con·cep·tu·al·ize
v. con·cep·tu·al·ized, con·cep·tu·al·iz·ing, con·cep·tu·al·iz·es
To form a concept or concepts of, and especially to interpret in a conceptual way: mathematics more in the way it is holistically practiced than as an abstract body of formalized for·mal·ize
tr.v. for·mal·ized, for·mal·iz·ing, for·mal·iz·es
1. To give a definite form or shape to.
a. To make formal.
b. theoretical results. Leach's outlook may also be questioned by evangelical Christian mathematicians, some of whom believe there is a more integral way to relate their faith to their professional work. But Mathematics and Religion does offer an informed discussion of the topic by a mathematician committed to faith in Jesus Christ, and as such provides a viewpoint readers can use to test and sharpen their own ideas on the relationships.
Reviewed by Calvin Jongsma, Professor of Mathematics, Dordt College, Sioux Center, IA 51250.